The document on the left was created with TextMaker 2018; the document on the right with LibreOffice 6.03. In the Textmaker document, the distance between the bold "Lorem Ipsum" and the horizontal line is significant and noticeable. In the LibreOffice document, the distance is much less, creating a more pleasing appearance. How can I get TextMaker to replicate this?

Probably the default settings for horizontal lines in your TextMaker and LibreOffice installations are different. How did you insert the line - via "Object > New drawing > Line"? In this case, just right-click the line, choose "Line properties..." from the context menu and make sure that in tab "Layout" "Text Wrapping" is set to "Behind text" or "In front of text". (If you want the line to flow with the text, position must be set "relative to paragraph" and "Move with text" must be checked.) Then you can adjust the position of the line with the arrow keys (Cmd+arrow key for smaller steps).